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Question
AD is drawn perpendicular to base BC of an equilateral triangle ABC. Given BC = 10 cm, find the length of AD, correct to 1 place of decimal.
Solution
Since ABC is an equilateral triangle therefore, all the sides of the triangle are of the same measure and the perpendicular AD will divide BC into two equal parts.
Pythagoras theorem states that in a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the remaining two sides.
Here, we consider the ΔABD and applying Pythagoras theorem we get,
AB2 = AD2 + BD2
AD2 = 102 - 52 ......[ Given, BC = 10 cm = AB, BD = `1/2` BC ]
AD2 = 100 - 25
AD2 = 75
AD = 8.7
Therefore, the length of AD is 8.7 cm
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